Question

value of cot(cot^-1(3)+cot^-1(7)+cot^-1(13)+cot^-1(1)+21) is?​

Answer 1

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value of cot(cot^-1(3)+cot^-1(7)+cot^-1(13)+cot^-1(1)+21) is?

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$cot[tan^{ - 1}( \frac{1}{3} ) + tan^{ - 1}( \frac{1}{7} ) + tan^{ - 1}( \frac{1}{13} ) + tan^{ - 1}( \frac{1}{21} )] \\ Using, \\ tan^{ - 1}x + tan^{ - 1}y = tan^{ - 1}[ \frac{(x + y)}{(1 - xy)}], \\ we \: get, \\cot[tan^{ - 1}( \frac{1}{2} ) + tan^{ - 1}( \frac{1}{8} )] = \frac{3}{2}$

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